All resource usage and/or pollution will
grow exponentially but with different couplings to the population
growth this is extremely relevant to
greenhouse gas emissions Run the Simulator

In general, decision making is done at the self-interest level.
With exponential resource usage, such decision making is extremely
destructive. What we need is convergence on the least "bad" option.

The ability to discern amoung
the least bad alternatives is extremely difficult. Politics and
pseudo-experts come into play. Science can help, but still the
process is quite inexact. The New Carissa accident is a good
example of this.

The self-interest decision making is encouraged because we do
a very bad job at "training" and educating people to look at the data.
We do an even worse job at presenting the raw data for objective
analysis. Instead, we are a nation and community of SPIN doctors.
This causes people to argue from a position of belief rather than
a position of knowledge.

Now, of course, the problem is made worse by the perception that we
are all afraid of math and that "formulas" don't apply to real life.

"Math, formulas and other things that don't apply to real life"

(--anonymous comment from student evaluation of Physics 161 course
as the part they liked least about the course)

So we live in a society that is afraid of and doesn't understand
numbers.

This again is a recipe for disaster as
it means the public can be sold most anything

An example:

A survey of Boulder Colorado residents about the optimal size for
growth returned a result that most residents thought that
a growth in population at the rate of 10% per year was desirable.

Well 10% a year may not seem innocuous but let's see how
these numbers would add up?

Year 1 60,000

Year 2 66,000

year 3 72,600

Year 4 79860

Year 5 87846

Year 6 96630

year 7 106294

Year 8 116923

So in 7 years (year 2--7) the population has doubled and by then
10,000 new residents per year are moving to Boulder!

Clearly, Exponential growth, in general, is not understood by
the lay public. If exponential use of a resource is
not accounted for in planning - disaster can happen.

The difference between linear growth and exponential
growth is astonishing.

In this example, one can clearly see that no matter what the growth
rate is, exponential growth stars out being in a period of slow
growth and then quickly changes over to rapid growth with
a characteristic doubling time of

70/n years; n =% growth rate

Its important to recognize that even in the slow growth period,
the use of the resource is exponential. If you fail to realize
that, you will run out of the resource pretty fast:

Material

Rate

Exhaustion Timescale

Aluminum

6.4%

2007 -- 2023

Coal

4.1%

2092 -- 2106

Cooper

4.6%

2001 -- 2020

Petroleum

3.9%

1997 -- 2017

Silver

2.7%

1989 -- 1997

The above estimates include recycling.

Exponential growth means that some quantity
grows by a fixed percentage rate from one year
to the next. A handy formula for calculating
the doubling time for exponential growth is:

Doubling Time = 70/n years

where n is the percentage growth rate. Thus, if the growth
rate is say 5%, the doubling time would be 14 years.